Unit 4-5 Assignment Improvement Course Part A: Knowledge (on D2L) Part B: Application 1. An airplane is flying at 400 km/h on a heading of 050". The wind is blowing at 30 km/h at a bearing of 153'. Determine the ground velocity of the airplane and the direction of flight. 2. A 200 N light fixture is held by two cables of equal length making angles of 70' below the ceiling. Determine the tensions in the cables. 3. Given the vectors a = 21 - / + 3kand b = 1 + 2/ - 2k, find: a) the angle between these two vectors (to one decimal) b) vector projection of a on b (exact value) 4. Find a vector orthogonal to both a = 87 - 37 + k and b = -1 - 97 + 5k. Verify. 5. A 45 kg box rests on a ramp that is inclined 37. Resolve the weight into rectangular vector components that keep the box at rest. Part C: Thinking 6. Imagine that you are in a boat travelling at a constant speed of 20 knots due east. The current is flowing from a bearing of $68'E at a speed of 5 knots and the headwind is blowing toward the west at a speed of 6 knots. Where will you end up? Include a diagram in your solution. 7. A triangle has vertices A (3, -2, 7), B (2,2, -3), and C (1, 1, 2). Classify the triangle as scalene, isosceles or equilateral. Is the triangle a right triangle? Show all steps in your solution